Narrow opposite-parity level crossings
in a diatomic free radical
Dave DeMille, E. Altuntas, J. Ammon, S.B. Cahn, R. Paolino*
Physics Department, Yale University
*Physics Department, US Coast Guard Academy
• Motivation: nuclear spin-dependent parity violation
• PV measurement strategy: Zeeman-tuned rotational degeneracies
• Measurements: Stark-induced transitions near a rotational level crossing
• Outlook
DeMille
Funding: NSF
Group
Mechanisms for atomic/molecular parity violation
Electroweak coupling to nuclear spin: “NSD-PV”
e
HW 
 ( Z  an ) 
3 
(I   )(  p )  (r )
e
Ve+Ae
e

Z0
+
I
VN+AN
N
NSD-PV from
direct Z0 exchange: +
numerically
suppressed
nuclear
spin I
Z0, W±
N
PV weak interactions
inside nucleus induce
nuclear “anapole moment”
that couples to electron
magnetically
Weak-interaction
Hamiltonian HW mixes
hyperfine states with
opposite parity
Enhanced parity mixing via systematic level
degeneracies in diatomic free radicals
Example: 2 with single nuclear spin I=1/2 (e.g. 138BaF)
Typically several crossings
for B = 0.3 - 1 T
JP
Rotation
+ e- spin 1/2
3/2-
+ nuclear spin
(I=1/2)
-
1-
1/2-
01+
1/2+
0+
2
1-
Effective energy separation
 ~ 1 kHz ~ 10-11 eV near crossing
 1011 enhancement vs. atoms!
B
The ZOMBIES NSD-PV experiment at Yale
Z eeman-tuned
O ptically prepared and detected
Molecular
B eams for the
Investigation of
E lectroweak effects using
S tark interference
Molecule PV experimental schematic
Superconducting solenoid
B
(1)
E0
(2)
(1)
(2)
(3)
(4)
(4)
(3)
E0
Laser
|->
Laser
|+>
Stark interference method:
apply oscillating -field to mix nearly-degenerate levels
Zeeman-shifted Energy E
Center of Magnet:
Homogeneity B/B < 10-7
D(B )
E
E+
Position z  Time t = z/v
Strategy to detect PV in near-degenerate levels
|->
D(B )
|+>
æ
ö÷

0
iH
d
(
t
)
+
ç
W
÷÷
H = çç
÷÷ø
D
çè-iHW +d(t)
w
0 sin(wt )
S = + y(T )
 (t ) = 0 sin(wt )
é w  D, d  ù
0û
ë
2
2
é
ù
æ
ö
æ
ö
HW d 0 ú
2 ç DT ÷ êçd 0 ÷
÷ +2
÷÷ êçç
= 4 sin ç
ú
÷
çè 2 ÷ø êçè w ø÷
D w ú
êë
úû
D.D., S.B. Cahn, D. Murphree, D.A. Rahmlow, and M.G. Kozlov
Phys. Rev. Lett. 100, 023003 (2008)
Large
Stark Term
Even in 0
Small
Weak Term
Odd in 0
Signal, Asymmetry, Sensitivity
2
é
ù
æ
ö
æ
ö
HW d 0 ú
2 ç DT ÷ êçd 0 ÷
÷÷ + 2
÷÷ êçç
--Measure signal S (0 ) » 4N 0 sin ç
ú
çè 2 ÷ø êçè w ø÷
D w ú
êë
úû
with opposite-sign  -fields +0, -0
--Form asymmetry to extract HW in terms of known quantities:
S (+0 ) - S (-0 ) HW w
=
»
D d 0
S (+0 ) + S (-0 )
Statistical Uncertainty
1
1 1
 HW 
2 2 N0 T
best sensitivity from
large interaction time T
with constant 
Experimental study of Stark-induced transitions
at level crossings in 138BaF
6550
|-1/2,
Energy (MHz)
|-1/2
,
6500
|-1/2,
|-1/2
1/2, -1/2,
|ms, mI, mN>
1>
mF=0
0>
1/2, 0
, -1/2
mF=+1
>
, 1>
,0
2
/
1
,
|1/2
6450
|1
6400
4600
mF=-1
,
2
/
1
/2,
>
0>
|-1/2
,
1/2,
4625
Magnetic Field (Gauss)
1>
4650
Opposite-parity level crossing spectroscopy
Apply unipolar E-field pulse
E-
-field from step potential
on cylindrical boundary
 (t )
D(B )
 0 e
t 2 /  2
-V
E+
+V
Simple Stark-induced transition at a level crossing
|->
D(B )
|+>
d  (t ) 
 0
H 

 
 d  (t )
 (t )  0 e
t 2 /  2
for weak excitation (dE0  1) , Gaussian lineshape:
S     c  t   
2

2
2/ 

d   e
2
2 2
0
2
Linewidth
1 / 
on resonance w/arbitrary excitation strength: Rabi flopping
S    0; 0   sin 2

 d 0

Typical level-crossing data: lineshape & position
B-field at crossing
from position of peak
S ()  e
Interaction time 
from width of peak
Matches calculated
FWHM  ~ 6 kHz
(kHz)
 2 2

2
Rabi flopping: period vs. 0 determines d
Peak normalized signal
[suppressed
Dipole matrix element d = 3574(7) Hz/(V/cm) by
spin flip]
Peak applied electric field 0 [V/cm]
Complex lineshapes from off-resonant Stark shifts
Apply single E-field pulse
E-
D(B, t )
Spatially-varying
detuning due to offresonant Stark shifts
 (t )  0 e
t 2 /  2
E+
Center of Magnet
Data: lineshapes from off-resonant Stark shifts
Data and fit including spatially-varying Stark shift
Fit at several different 0 values determines
crossing position vs. B, and Stark shift strength
Calculated level crossings in
6550
|ms, mI, mN>
|-1/2,
1/2, -1
Energy (M H z)
|-1/2,
6500
-1/2,
|-1/2,
|-1/2,
138BaF
>
mF=0
0>
1/2, 0
-1/2,
mF=-1
mF=+1
>
1>
, 0>
2
/
1
,
|1/2
6450
2, 0
/
1
,
|1/2
6400
4600
>
|-1/2,
1/2, 1
4625
Magnetic Field (Gauss)
>
4650
16
Extracted data from 138BaF crossings:
crossing positions & dipole matrix elements
Type
Initial Calc.X
Obs. X
(Gauss)
(Gauss)
Calc. d Obs. d
Unc.obs.
(Hz/V/cm) (Hz/V/cm) (Hz/V/cm)
Generally excellent agreement with all predictions from standard
spin/rotation/hyperfine + Zeeman Hamiltonian treatment;
some details still to be completed in fit
Initial, very preliminary NSD-PV data in
Shaped -field
Normalized Signal S
æ DT ÷ö
ç
÷
S = 4 sin ç
çè 2 ÷÷ø
2
éæ
ù
ö
d
H
d


ê
ú
´ êççç 0 ÷÷÷ + 2 W 0 ú
D w ú
êèç w ÷ø
êë
úû
2
 (t ) =
0 sin(wt )
0.4
138BaF
0.3
0.2
0.1
Take NSD-PV
data HERE
a
Positive E0
Negative E0
0
‐10
‐5
0
Detuning  (kHz)
5
10
Conclusions & Outlook:
Parity Violation with Diatomic Free Radicals
•
Opposite-parity level-crossing spectroscopy:
linewidth (as small as 4 kHz), lineshapes, positions, matrix
elements, etc. all in agreement with theory
•
Molecular systems very promising for study of NSD-PV:
excellent S/N & systematics, leverage from developed techniques
•
Multiple nuclei available for anapole moment determination
(we will use 137Ba in 137BaF first; 19F in 138BaF now for testing)
•
Measurements of fundamental Z0 couplings possible in long term?
•
Likely extensions with new molecular data, improved molecular
beams, laser cooling, etc: an “anapole factory”…?
•
n.b. same level crossings suggested for simulation of conical
intersections in trapped ultracold molecules [Hutson, Krems, etc.]
Emine Altuntas
Jeff Ammon
John Barry
Colin Bruzewicz
Sid Cahn, PhD
Eustace Edwards
Danny McCarron,PhD
Eric Norrgard
Brendon O’Leary
Toshihiko Shimasaki
Matt Steinecker
Adam West, Ph.D
DeMille
Group
Prof. Rich Paolino
US Coast Guard Academy